To me the OP isn't describing a "dirty house". I think, at the very least, children deserve a bathroom they can get clean and eliminate in safely, a countertop to make a pb&j on without pushing aside animal droppings, and to live in a home that isn't strewn with "beer cans everywhere". Sounds like mental health and possibly substance abuse issues -- and while I don't know as I would call as my first reaction, just by the information the OP's shared, no way I would call this mom a "really good" mom.
It's difficult not to judge when someone (I assume by the info OP has provided) has been helped time and again by concerned friends and family members, has financial resources and caring people in their life, and still refuses to care for their children the way they deserve.
I agree. I know it's easy to see this from the mother's side, but mom needs help. It sounds like what you hear about on the show Hoarders where they need to have help breaking through that mental barrier in the situation which is probably depression. They can set her up with that. What about calling Adult Protective Services to get her the help she needs and the clean up may follow?
And I know that kids love their parents unconditionally, but is it really fair to ask a child to live in filth? Tumble described it perfectly. My house isn't spotless but what is being describes is unsanitary and could be bad for the children's long-term health. Who is the voice of the child here? How can we expect a child to see their mom as "not doing a good enough job?"
I've never called CPS on anyone so I am only going on what the OP is saying